Question

For what value of p are 2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.?

Answer 1

Answer:

The value of p is 4 .

Step-by-step explanation:

Given :  

2p + 1, 13, 5p – 3 are three consecutive terms of an A.P.

Let a1 = 2p + 1 , a2 = 13 and a3 = 5p – 3

If Terms are in A.P, then the common difference (d) of any two consecutive terms is same.  

⇒ a2 - a1 = a3 - a2

⇒ 13 - (2p + 1) = 5p - 3 - 13

⇒ 13 - 2p - 1 = 5p –3 –13

⇒12– 2p = 5p –16

⇒12 + 16 = 5p + 2p

⇒ 28 = 7p

⇒ p = 28/7

⇒ p = 4

Hence, the value of p is 4 .

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Answer 2

Answer:

P = 4

Step-by-step explanation:

2p + 1, 13, 5p − 3 are three consecutive terms of an A.P.

So,

=> d1 = d2

=> 13-2p-1 = 5p-3-13

=> 12-2p = 5p - 16

=> 5p+2p = 12+16

=> 7p = 28

=> p = 28/7 = 4 Ans